

It is Mikhailov [1]} who first gave a Lax pair of the massive Thirring model, for () which reads
[1]}, [3]}
\(& \Phi _{x_0}=M_0\Phi ,~~M_0=\frac{i}{2}\left(\begin{array}{cc}-|\mathcal {X}_1|^2+|\mathcal {X}_2|^2-\lambda ^2+\lambda ^{-2}& 2\lambda \mathcal {X}_2^*-2\lambda ^{-1}\mathcal {X}^*_1\\2\lambda \mathcal {X}_2-2\lambda ^{-1}\mathcal {X}_1& |\mathcal {X}_1|^2-|\mathcal {X}_2|^2+\lambda ^2-\lambda ^{-2}\end{array}\right),\\& \Phi _{x_1}=M_1\Phi ,~~M_1=\frac{i}{2}\left(\begin{array}{cc}|\mathcal {X}_1|^2+|\mathcal {X}_2|^2-\lambda ^2-\lambda ^{-2}& 2\lambda \mathcal {X}_2^*+2\lambda ^{-1}\mathcal {X}^*_1\\2\lambda \mathcal {X}_2+2\lambda ^{-1}\mathcal {X}_1& -|\mathcal {X}_1|^2-|\mathcal {X}_2|^2+\lambda ^2+\lambda ^{-2}\end{array}\right),\) 
